arXiv subjects

Hans-Thomas Elze

Publications and source records attributed to Hans-Thomas Elze.

At least 37 records · Page 2Linked to original sources

arXiv2013

Discrete mechanics, time machines and hybrid systems

Modifying the discrete mechanics proposed by T.D. Lee, we construct a class of discrete classical Hamiltonian systems, in which time is one of the dynamical variables. This includes a toy model of time machines which can travel forward and backward in time and which differ from models based on closed timelike curves (CTCs). In the continuum limit, we explore the interaction between such time reversing machines and quantum mechanical objects, employing a recent description of quantum-classical hybrids.

quant-ph↗

arXiv2013

Quantum-classical hybrid dynamics - a summary

A summary of a recently proposed description of quantum-classical hybrids is presented, which concerns quantum and classical degrees of freedom of a composite object that interact directly with each other. This is based on notions of classical Hamiltonian mechanics suitably extended to quantum mechanics.

quant-ph↗

arXiv2012

Proliferation of observables and measurement in quantum-classical hybrids

Following a review of quantum-classical hybrid dynamics, we discuss the ensuing proliferation of observables and relate it to measurements of (would-be) quantum mechanical degrees of freedom performed by (would-be) classical ones (if they were separable). -- Hybrids consist in coupled classical ("CL") and quantum mechanical ("QM") objects. Numerous consistency requirements for their description have been discussed and are fulfilled here. We summarize a representation of quantum mechanics in terms of classical analytical mechanics which is naturally extended to QM-CL hybrids. This framework allows for superposition, separable, and entangled states originating in the QM sector, admits experimenter's "Free Will", and is local and non-signalling. -- Presently, we study the set of hybrid observables, which is larger than the Cartesian product of QM and CL observables of its components; yet it is smaller than a corresponding product of all-classical observables. Thus, quantumness and classicality infect each other.

quant-ph↗

arXiv2012

Linear dynamics of quantum-classical hybrids

A formulation of quantum-classical hybrid dynamics is presented, which concerns the direct coupling of classical and quantum mechanical degrees of freedom. It is of interest for applications in quantum mechanical approximation schemes and may be relevant for the foundations of quantum mechanics, in particular, when it comes to experiments exploring the quantum-classical border. The present linear theory differs from the nonlinear ensemble theory of Hall and Reginatto, but shares with it to fullfill all consistency requirements discussed in the literature, while earlier attempts failed in this respect. Our work is based on the representation of quantum mechanics in the framework of classical analytical mechanics by A. Heslot, showing that notions of states in phase space, observables, Poisson brackets, and related canonical transformations can be naturally extended to quantum mechanics. This is suitably generalized for quantum-classical hybrids here.

quant-ph↗

arXiv2012

Four questions for quantum-classical hybrid theory

Four questions are discussed which may be addressed to any proposal of a quantum-classical hybrid theory which concerns the direct coupling of classical and quantum mechanical degrees of freedom. In particular, we consider the formulation of hybrid dynamics presented recently in Ref.[1]. This linear theory differs from the nonlinear ensemble theory of Hall and Reginatto, but shares with it to fulfil all consistency requirements discussed in the literature, while earlier attempts failed. - Here, we additionally ask: Does the theory allow for superposition, separable, and entangled states originating in the quantum mechanical sector? Does it allow for "Free Will", as introduced, in this context, by Diosi [2]. Is it local? Does it provide hints for the emergence of quantum mechanics from dynamics beneath?

quant-ph↗

arXiv2010

A path integral for classical dynamics, entanglement, and Jaynes-Cummings model at the quantum-classical divide

The Liouville equation differs from the von Neumann equation 'only' by a characteristic superoperator. We demonstrate this for Hamiltonian dynamics, in general, and for the Jaynes-Cummings model, in particular. -- Employing superspace (instead of Hilbert space), we describe time evolution of density matrices in terms of path integrals which are formally identical for quantum and classical mechanics. They only differ by the interaction contributing to the action. This allows to import tools developed for Feynman path integrals, in order to deal with superoperators instead of quantum mechanical commutators in real time evolution. Perturbation theory is derived. Besides applications in classical statistical physics, the "classical path integral" and the parallel study of classical and quantum evolution indicate new aspects of (dynamically assisted) entanglement (generation). Our findings suggest to distinguish 'intra'- from 'inter-space' entanglement.

quant-ph↗

arXiv2010

Spacetime and Matter - a duality of partial orders

A new kind of duality between the deep structures of spacetime and matter is proposed here, considering two partial orders which incorporate causality, extensity, and discreteness. This may have surprising consequences for the emergence of quantum mechanics, which are discussed.

gr-qc↗

arXiv2009

Does quantum mechanics tell an atomistic spacetime?

The canonical answer to the question posed is "Yes." -- tacitly assuming that quantum theory and the concept of spacetime are to be unified by `quantizing' a theory of gravitation. Yet, instead, one may ponder: Could quantum mechanics arise as a coarse-grained reflection of the atomistic nature of spacetime? -- We speculate that this may indeed be the case. We recall the similarity between evolution of classical and quantum mechanical ensembles, according to Liouville and von Neumann equation, respectively. The classical and quantum mechanical equations are indistinguishable for objects which are free or subject to spatially constant but possibly time dependent, or harmonic forces, if represented appropriately. This result suggests a way to incorporate anharmonic interactions, including fluctuations which are tentatively related to the underlying discreteness of spacetime. Being linear and local at the quantum mechanical level, the model offers a decoherence and natural localization mechanism. However, the relation to primordial deterministic degrees of freedom is nonlocal.

quant-ph↗

arXiv2008

The Attractor and the Quantum States

The dissipative dynamics anticipated in the proof of 't Hooft's existence theorem -- "For any quantum system there exists at least one deterministic model that reproduces all its dynamics after prequantization" -- is constructed here explicitly. We propose a generalization of Liouville's classical phase space equation, incorporating dissipation and diffusion, and demonstrate that it describes the emergence of quantum states and their dynamics in the Schroedinger picture. Asymptotically, there is a stable ground state and two decoupled sets of degrees of freedom, which transform into each other under the energy-parity symmetry of Kaplan and Sundrum. They recover the familiar Hilbert space and its dual. Expectations of observables are shown to agree with the Born rule, which is not imposed a priori. This attractor mechanism is applicable in the presence of interactions, to few-body or field theories in particular.

quant-ph↗

arXiv2008

Note on the existence theorem in ``Emergent Quantum Mechanics and Emergent Symmetries''

Recently 't Hooft demonstrated that ``For any quantum system there exists at least one deterministic model that reproduces all its dynamics after prequantization''. An extension is presented here which covers quantum systems that are characterized by a complete set of mutually commuting Hermitian operators (``beables''). We introduce the symmetry of beables: any complete set of beables is as good as any other one which is obtained through a real general linear group transformation. The quantum numbers of a specific set are related to symmetry breaking initial and boundary conditions in a deterministic model. The Hamiltonian, in particular, can be taken as the emergent beable which provides the best resolution of the evolution of the model universe.

quant-ph↗

arXiv2007

A relativistic gauge theory of nonlinear quantum mechanics and Newtonian gravity

A new kind of gauge theory is introduced, where the minimal coupling and corresponding covariant derivatives are defined in the space of functions pertaining to the functional Schroedinger picture of a given field theory. While, for simplicity, we study the example of a U(1) symmetry, this kind of gauge theory can accommodate other symmetries as well. We consider the resulting relativistic nonlinear extension of quantum mechanics and show that it incorporates gravity in the (0+1)-dimensional limit, similar to recently studied Schroedinger-Newton equations. Gravity is encoded here into a universal nonlinear extension of quantum theory. A probabilistic interpretation (Born's rule) holds, provided the underlying model is scale free. Keywords: nonlinear functional Schroedinger equation, gauge symmetry, Newtonian gravity.

gr-qc↗

arXiv2007

Is there a relativistic nonlinear generalization of quantum mechanics?

Yes, there is. - A new kind of gauge theory is introduced, where the minimal coupling and corresponding covariant derivatives are defined in the space of functions pertaining to the functional Schroedinger picture of a given field theory. While, for simplicity, we study the example of an U(1) symmetry, this kind of gauge theory can accommodate other symmetries as well. We consider the resulting relativistic nonlinear extension of quantum mechanics and show that it incorporates gravity in the (0+1)-dimensional limit, where it leads to the Schroedinger-Newton equations. Gravity is encoded here into a universal nonlinear extension of quantum theory. The probabilistic interpretation, i.e. Born's rule, holds provided the underlying model has only dimensionless parameters.

quant-ph↗

arXiv2007

Quantum fields, cosmological constant and symmetry doubling

Energy-parity has been introduced by Kaplan and Sundrum as a protective symmetry that suppresses matter contributions to the cosmological constant [KS05]. It is shown here that this symmetry, schematically Energy --> - Energy, arises in the Hilbert space representation of the classical phase space dynamics of matter. Consistently with energy-parity and gauge symmetry, we generalize the Liouville operator and allow a varying gauge coupling, as in "varying alpha" or dilaton models. In this model, classical matter fields can dynamically turn into quantum fields (Schroedinger picture), accompanied by a gauge symmetry change -- presently, U(1) --> U(1) x U(1). The transition between classical ensemble theory and quantum field theory is governed by the varying coupling, in terms of a one-parameter deformation of either limit. These corrections introduce diffusion and dissipation, leading to decoherence.

hep-th↗

arXiv2006

The Gauge Symmetry of the Third Kind and Quantum Mechanics as an Infrared Limit

We introduce functional degrees of freedom by a new gauge principle related to the phase of the wave functional. Thus, quantum mechanical systems are dissipatively embedded into a nonlinear classical dynamical structure. There is a necessary fundamental length, besides an entropy/area parameter, and standard couplings. For states that are sufficiently spread over configuration space, quantum field theory is recovered.

hep-th↗

arXiv2006

Gauge Symmetry of the Third Kind and Quantum Mechanics as an Infrared Phenomenon

We introduce functional degrees of freedom by a new gauge principle related to the phase of the wave functional. Thereby, quantum mechanical systems are seen as dissipatively embedded part of a nonlinear classical structure producing universal correlations. There are a fundamental length and an entropy/area parameter, besides standard couplings. For states that are sufficiently spread over configuration space, quantum field theory is recovered.

quant-ph↗

arXiv2005

Deterministic models of quantum fields

Deterministic dynamical models are discussed which can be described in quantum mechanical terms. -- In particular, a local quantum field theory is presented which is a supersymmetric classical model. The Hilbert space approach of Koopman and von Neumann is used to study the classical evolution of an ensemble of such systems. Its Liouville operator is decomposed into two contributions, with positive and negative spectrum, respectively. The unstable negative part is eliminated by a constraint on physical states, which is invariant under the Hamiltonian flow. Thus, choosing suitable variables, the classical Liouville equation becomes a functional Schroedinger equation of a genuine quantum field theory. -- We briefly mention an U(1) gauge theory with ``varying alpha'' or dilaton coupling where a corresponding quantized theory emerges in the phase space approach. It is energy-parity symmetric and, therefore, a prototype of a model in which the cosmological constant is protected by a symmetry.

gr-qc↗

arXiv2005

A quantum field theory as emergent description of constrained supersymmetric classical dynamics

Deterministic dynamical models are discussed which can be described in quantum mechanical terms. In particular, a local quantum field theory is presented which is a supersymmetric classical model. -- The Hilbert space approach of Koopman and von Neumann is used to study the evolution of an ensemble of such classical systems. With the help of the supersymmetry algebra, the corresponding Liouville operator can be decomposed into two contributions, with positive and negative spectrum, respectively. The unstable negative part is eliminated by a constraint on physical states, which is invariant under the Hamiltonian flow. In this way, choosing suitable phase space coordinates, the classical Liouville equation becomes a functional Schroedinger equation of a genuine quantum field theory. Quantization here is intimately related to the constraint, which selects the part of Hilbert space where the Hamilton operator is positive. This is interpreted as dynamical symmetry breaking in an extended model, introducing a mass scale which discriminates classical dynamics beneath from emergent quantum mechanical behaviour.

hep-th↗

arXiv2005

Determinism and a supersymmetric classical model of quantum fields

A quantum field theory is described which is a supersymmetric classical model. -- Supersymmetry generators of the system are used to split its Liouville operator into two contributions, with positive and negative spectrum, respectively. The unstable negative part is eliminated by a positivity constraint on physical states, which is invariant under the classical Hamiltonian flow. In this way, the classical Liouville equation becomes a functional Schroedinger equation of a genuine quantum field theory. Thus, 't Hooft's proposal to reconstruct quantum theory as emergent from an underlying deterministic system, is realized here for a field theory. Quantization is intimately related to the constraint, which selects the part of Hilbert space where the Hamilton operator is positive. This is seen as dynamical symmetry breaking in a suitably extended model, depending on a mass scale which discriminates classical dynamics beneath from emergent quantum mechanical behaviour.

hep-th↗